移动简谐力作用下三维多孔饱和半空间的动力问题

DYNAMIC PROBLEMS OF A POROELASTIC HALF SPACE SUBJECTED TO A HARMONICALLY MOVING LOAD

研究了移动荷载作用下多孔饱和地基的动力问题.应用Fourier变换求解该问题的控制偏微分方程,考虑了荷载的移动速度及振动频率对多孔饱和地基动力响应的影响,重点研究了移动速度达地基表面波速时多孔饱和半空间的振动问题(马赫效应),并与相应的弹性介质的解答进行了比较.结果显示当移动速度与多孔饱和半空间的表面波速相近时,地基会产生很大的振动;当移动速度大于表面波速时,多孔饱和半空间的动力响应与弹性半空间的动力响应有较大的差别.

This paper considers the dynamic problems of a poroelastic half space subjected to a harmonically moving load. The solutions of Biot＇s dynamic equations are obtained through the Fourier Transform Method. Effects of the velocity and the harmonic frequency of an external moving load on the dynamic responses of a poroelastic half space are numerically studied in detail. The obtained results are compared with the classical elasticity solutions. When the load velocity approaches to the Rayleigh speed of the medium, the Mach effect is especially discussed. It follows from the analysis that the displacements, stresses and pore pressure reach the maxima when the load velocity approaches the Rayleigh speed, and moreover, it is found that both the velocity and the harmonical frequency of a moving load have significant influence on the dynamic charactersitics of a poroelastic half space. The poroelastic solutions differ substantially from the ideal elastic solutions when the load velocity is in the transonic range. Therefore, incorporation of poroelastic behavior is important in study of the response of a poroelastic half space caused by a high speed train.